Noetherian
From Wikipedia, the free encyclopedia
In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending or descending chain condition on certain kinds of subobjects; in particular,
- Noetherian ring, a ring that satisfies the ascending chain condition on ideals.
- Noetherian module, a module that satisfies the ascending chain condition on submodules.
- Noetherian topological space, a topological space that satisfies the descending chain condition on closed sets.
See also:
- Emmy Noether, who was the first to study the ascending and descending chain conditions for rings, and for whom the term is named.
- Artinian ring, a ring that satisfies the descending chain condition on ideals.
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